Assessing R2 Contributions:

Role of Weighted Path Length

PLedge 1to5

Low R2

High R2

PLedge 1-6to10

Low R2

High R2

PLedge 1-11to14

Low R2

High R2

Summary reflections

  • There is no consistent pattern such that lower (or higher) path edge values are significantly differentiated from higher (or lower) path edge values.
  • That is, the functional connectivity values at lower and higher path length edges are the same.
  • This suggests that the weight of direct path length edges (PLedge=1) is roughly equal to the total weight of multi-hop path length edges (PLedge > 1), especially for higher R2 contributions toward functional connectivity.

Best Model Evaluation

No Communicability Model [SIC01]

Differences in R2 Total Brain Maps with and without Communicability (CO)

No Path Length Model [SIC01]

Differences in R2 Total Brain Maps with and without Weighted Path Length (PL)

To-Dos

  • Check if similar R2 brain maps are generated for SIC02 and SIC03
  • Rerun section on: Role of Weighted Path Length with Binarized Version (and only for f~ed + co)

Checks

Linear Model or Other?

Is a linear model appropriate?   - A linear model might offer the simplest explanation across a range of ROI models. Best to go with pl split and see what happens. - f ~ ed + co not definitely superior to f ~ed + pl when looking at each ROI individually (that is, there is lot of variability)

Some references to consider   - http://www.sthda.com/english/articles/39-regression-model-diagnostics/161-linear-regression-assumptions-and-diagnostics-in-r-essentials/ - https://stats.stackexchange.com/questions/32781/how-can-i-use-the-value-of-r2-to-test-the-linearity-assumption-in-multiple-re - https://stats.stackexchange.com/questions/530206/multiple-linear-regression-assumptions - https://medium.com/datasciencearth/r-applications-part-2-multiple-linear-regression-d3d5d63c4627 - https://stackoverflow.com/questions/43837088/how-to-write-a-function-to-check-model-assumptions-for-a-linear-model-in-r - https://ajstewartlang.github.io/10_glm_regression_pt2/knitted_workshop/10_glm_regression_pt2.html#Dropping_an_Influential_Case - https://github.com/rempsyc/rempsyc/blob/8e2b4f5bd6a5e52abec3cd58057ca450a26ceab9/R/nice_assumptions.R

 

## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##   
## Interpretation: (p) values < .05 imply assumptions are not respected. 
## Diagnostic is how many assumptions are not respected for a given model or variable. 
##